zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Pullback attractors of nonautonomous and stochastic multivalued dynamical systems. (English) Zbl 1018.37048
The existence of pullback global attractors for multivalued processes generated by differential inclusions is studied. Mainly one deals with nonautonomous multivalued dynamical systems in which the trajectories can be unbounded in time and with nonautonomous stochastic multivalued dynamical systems. Let $X$ be a complete metric space, $P(X)$ the set of all subsets of $X$. Denote $\bbfR_d= \{(t,s)\in \bbfR^z:t\ge s\}$. The map $U:\bbfR_d\times X \to P(X)$ is called a multivalued dynamical process (MDP) on $X$ if 1) $U(t,t, \cdot)$ is the identical map, 2) $U(t,s,x)\subset U(t,\tau,U (\tau,s,x))$, $x\in X$, $s<\tau <t$. At first the authors proved abstract results on the existence of $\omega$-limit sets and global attractors and studied their topological properties (compactness, connectedness). Then they applied the abstract results to nonautonomous differential inclusions of the reaction-diffusion type in which the forcing term can grow polynomially in time and they gave applications to stochastic differential inclusions with additive and multiplicative noises. MDP is defined as a two-parameter family of multivalued maps. The attraction of any bounded set of the phase space to the global attractor is uniform with respect to the first parameter. The rate of attraction and the attractor itself can depend on the second parameter. The theory is extended to the cases with stochastic terms in the model.

37L55Infinite-dimensional random dynamical systems; stochastic equations
35B41Attractors (PDE)
35K55Nonlinear parabolic equations
35K57Reaction-diffusion equations
Full Text: DOI